A numerical approach for modelling variable stator stagger in multistage stage axial flow compressors is presented. The development of such an approach has been motivated by the requirements of an optimisation methodology for stator vane setting and active control of instability using controlled stator vane setting. The optimisation methodology has been further developed but active control approaches are discussed as future considerations. Varying upstream stator vane stagger . changes the incident flow angle on . the downstream rotor thus affecting the entire flow distribution within the compression systems. The approach therefore begins by investigating the effect of a change in stator stagger setting on stage performance. A meanline method was used for nu- merical prediction of stage characteristics as it can simulate the effect of a change in stagger settings and ( or) in rotational speeds. Overall compressor performance was obtained by stacking the (experimental or predicted) stage characteristics and the surge conditions predicted using a stage-by-stage dynamic compression model where the compressibility was considered explicitly. This approach for variable stagger set- ting was incorporated into a FORTRAN code and validated using the data from the 12-stage HP SPEY jTAY variable geometry compressor. To optimise the setting, a direct search method incorporating a Sequential Weight Increasing Factor Technique (SWIFT) algorithm was incorporated into the variable stagger model. The objective function in this optimisation is penalised externally 11 with an updated factor which helped to accelerate convergence. The methodology has been incorporated into a FORTRAN program and its validations were conducted using the data from the 7-stage LP OLYMPUS and the 12-stage HP SPEY /TAY compressors. Results have demonstrated that variable stagger setting is a powerful method to rematch stages and which can be used to improve the desired overall performance, and that the potential benefits of introducing additional rows of variable setting vanes can be achieved. Future work arising from the present study has been discussed and highlighted, which involves the enhancement of the model capacity and development of active control approaches. In addition the thesis involves several reviews focusing on different topics. Most reviews contain considerable information and it is expected that the information can be of help for the interested readers to trace more relevant references. These reviews consist of a general review in chapter 1; a brief review on stage characteristics modelling in chapter 2; a comparative review on incompressible and compressible surge models in chapter 3; a review of various optimisation methods for practical problems, especially for constrained non-smooth problems, in chapter 4; and a review of the state-of-the-art active approaches in chapter 7. The suitability of various approaches has been highlighted. Steinke's meanline method is suitable for investigating the in- influence of stagger resetting on stage performance. To predict the surge conditions for a (high-speed) multistage environment, the stage-by-stage compressible models are III more promising. For constrained non-smoothed optimisation, the SWIFT algorithm can be an alternative. The controlled stator vane regulated through nonlinear control law will permit the robust control of compressor instabilities.